On geometrically finite degenerations II: Convergence and divergence

@inproceedings{Luo2022OnGF,
  title={On geometrically finite degenerations II: Convergence and divergence},
  author={Yusheng Luo},
  year={2022}
}
In this paper, we study quasi post-critically finite degenerations for rational maps. We construct limits for such degenerations as geometrically finite rational maps on a finite tree of Riemann spheres. We prove the boundedness for such degenerations of hyperbolic rational maps with Sierpinski carpet Julia set and give criteria for the convergence for quasi-Blaschke products QBd, making progress towards the analogues of Thurston’s compactness theorem for acylindrical 3manifold and the double… 
On geometrically finite degenerations I: boundaries of main hyperbolic components
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In a previous paper [LLM20], we constructed an explicit dynamical correspondence between certain Kleinian reflection groups and certain anti-holomorphic rational maps on the Riemann sphere. In this
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